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4. Determine whether the pairs of functions are linearly independent or linearly dependent on the real line. a) f(x) = π, g(x) = cos²(x) + sin²(x) b) f(x) = x¹, g(x) = x³ |x|

4. Determine whether the pairs of functions are linearly independent or linearly dependent on the real line. a) f(x) = π, g(x) = cos²(x) + sin²(x) b) f(x) = x¹, g(x) = x³ |x|

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I only need help with parts a and b. Please show all steps clearly. Thank you. 

4. Determine whether the pairs of functions are linearly independent or linearly dependent on the real line. a) f(x) = π, g(x) = cos²(x) + sin²(x) b) f(x) = x¹, g(x) = x³|x| c) f(x) = e sinx, g(x) = e cos x d) f(x) = 3 sinx+ 2 cos x, g(x) = -2 sin x + 3 cos x
Transcribed Image Text:4. Determine whether the pairs of functions are linearly independent or linearly dependent on the real line. a) f(x) = π, g(x) = cos²(x) + sin²(x) b) f(x) = x¹, g(x) = x³|x| c) f(x) = e sinx, g(x) = e cos x d) f(x) = 3 sinx+ 2 cos x, g(x) = -2 sin x + 3 cos x
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